O is the centre of the circle. A tangent is drawn which touches the circle at C. If ∠AOC = 80º, then what is the value (in degrees) of ∠BCX?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 50
∠AOC = 80° [Given]
AC is a chord to the circle:
⇒ ∠ABC = 1/2 × ∠AOC = 1/2 × 80 = 40°
In triangle OBC:
OB = OC = radius of the circle
⇒ ∠OBC = ∠OCB = 40°
⇒ ∠XCO = 90° [Tangent is perpendicular to the radius]
⇒ ∠BCX = ∠XCO – ∠OCB = 90 – 40 = 50°